What is the extreme f(x)=-8x^3+24x+9 ?

The extreme f(x)=-8x^3+24x+9 is Minimum(-1,-7),Maximum(1,25)

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extreme f(x)=-8x^3+24x+9

extreme

Minimum (- 1, - 7), Maximum (1, 25)

Solution steps

f^{'} (x) = - 24 x^{2} + 24

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

- 8 x^{3} + 24 x + 9 : - 7

Minimum (- 1, - 7)

Plug

x = 1

into

- 8 x^{3} + 24 x + 9 : 25

Maximum (1, 25)

Minimum (- 1, - 7), Maximum (1, 25)

What is the extreme f(x)=-8x^3+24x+9 ?
The extreme f(x)=-8x^3+24x+9 is Minimum(-1,-7),Maximum(1,25)